{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GGXDWWXV3WWUM4RDUA5BSEHRPI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c49c18bd50df038a8c8788a22e72ad1ba15540c454815fdfe671e13cfe260d82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-13T01:21:33Z","title_canon_sha256":"890be895c546d5ccc4b18796e4091fc2b51e67ef560e45a4e5adcd53117b5ef4"},"schema_version":"1.0","source":{"id":"1408.2897","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2897","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2897v1","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2897","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"GGXDWWXV3WWU","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GGXDWWXV3WWUM4RD","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GGXDWWXV","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:c38458015e8ccca117ccb094f376154ca98b2b90eb7c478497dd13cece117d49","target":"graph","created_at":"2026-05-18T02:45:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the reverse mathematics and computability-the\\-o\\-re\\-tic strength of (stable) Ramsey's Theorem for pairs and the related principles COH and DNR. We show that SRT$^2_2$ implies DNR over RCA$_0$ but COH does not, and answer a question of Mileti by showing that every computable stable $2$-coloring of pairs has an incomplete $\\Delta^0_2$ infinite homogeneous set. We also give some extensions of the latter result, and relate it to potential approaches to showing that SRT$^2_2$ does not imply RT$^2_2$.","authors_text":"Bj{\\o}rn Kjos-Hanssen, Carl G. Jockusch, Denis R. Hirschfeldt, Steffen Lempp, Theodore A. Slaman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-13T01:21:33Z","title":"The Strength of Some Combinatorial Principles Related to Ramsey's Theorem for Pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2897","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ed7760d54882c4f381e82ef966be4dc6a4f71487e93bde21700b29aa839e7316","target":"record","created_at":"2026-05-18T02:45:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c49c18bd50df038a8c8788a22e72ad1ba15540c454815fdfe671e13cfe260d82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-13T01:21:33Z","title_canon_sha256":"890be895c546d5ccc4b18796e4091fc2b51e67ef560e45a4e5adcd53117b5ef4"},"schema_version":"1.0","source":{"id":"1408.2897","kind":"arxiv","version":1}},"canonical_sha256":"31ae3b5af5ddad467223a03a1910f17a075cc798442caaaa485e71beb63a19d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31ae3b5af5ddad467223a03a1910f17a075cc798442caaaa485e71beb63a19d4","first_computed_at":"2026-05-18T02:45:21.004134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:21.004134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Ooq9JE8AARma3Rbj7P7YW54iqCMKac4zCt9CM8GovAaI4PdzFXejhvJtExlJQML6LgmvWruLO0Ifwjq6QXgAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:21.004587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.2897","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed7760d54882c4f381e82ef966be4dc6a4f71487e93bde21700b29aa839e7316","sha256:c38458015e8ccca117ccb094f376154ca98b2b90eb7c478497dd13cece117d49"],"state_sha256":"f51dc32ffa9a91f0baa2fa8f726ee698e30b47711133fe76f5aa8206c034ed2c"}